Calculate the volume occupied by `2.0 mol` of `N_(2)` at `200 K` and `10.1325MPa` pressure if `(P_(c)V_(c))/(RT_(c))=(3)/(8)` and `(P_(r)V_(r))/(T_(r))=2.21`.

Explanation

Since `(P_(c)V_(c))/(RT_(c)) =(3)/(8)` and `(P_(r)V_(r))/(T_(r))=2.21`
`(P_(c)V_(c))/(RT_(c)) xx (P_(r)V_(r))/(T_(r))=(3)/(8)xx2.21`
or `(PV_(m))/(RT)=(3)/(8)xx2.21`
`:. V_(m)=((3)/(8)xx2.21)(RT)/(P)`
`=((3)/(8)xx2.21)((8.314MPa cm^(3)K^(-1)mol^(-1))(200 K))/((10.1325MPa))`
`=136.0cm^(3)mol^(-1)`
Hence, the volume of `2 mol` of `N_(2)` is `(2.0 mol)(136.0 cm^(3)mol^(-1))=272.0 cm^(3)`